"Neither one of our parents ever taught us to be bigoted toward any other person for any reason," the 43-year-old Bobby says, who is the host of the Cooking Channel series, Not My Mama's Meals. He refers to the allegations as "character assassination."

"Our mother is one of the most compassionate, good-hearted, empathetic people that you'd ever meet," Bobby continues. "These accusations are very hurtful to her, and it's very sad."

Jamie concurs, pointing out that he didn't hear the N-word used in their home when they were growing up.

It's "ridiculous, completely absurd to think there is an environment of racism in our business, and it's really disrespectful to the people that we work with," the 45-year-old Jamie says, who hosts Food Network's Home for Dinner with Jamie Deen.

"That word — that horrifying, terrible word that exists and I abhor it coming from any person — we weren't raised in a home where that word was used," he adds.